Horus BA has been considered another one of those local Lower Egyptian predecessors of Hotepsekhemwy, maybe mistaking his name with the possible name of "Bird" (Kaplony in MDAIK 20, 1965, p.3 proposes Ba as the reading of that bird sign in a serekh). For a "Horus Bird" possibly after Qa'a and Sneferka, cf. Sneferka.
Nabil Swelim (1983) and, more recently, Jochem Kahl (1994) have proposed a different chronological position for Ba, respectively in the early and in the late III rd Dynasty). Here I consider Ba as a possible Third Dynasty ruler or, alternatively, the Horus name of one of the ephemeral Memphite rulers of middle Second Dynasty (Wneg, Sened, Nwbnefer, Neferkasokar) known to us only by their Nebty-Nswtbity names.
The best source for the two documents concerning Ba is N. Swelim's 'Some Problems...' 1983 (cfr. bibliogr.).
Ba is attested in a serekh on a little basalt slab found by Firth at the Step Pyramid complex (not inserted in the publication) which was recorded only many years later by Goneim (Saqqara register of antiquities n. S-10034). It was composed by the signs of the human leg (B) + ram (BA)* (Gard. D58 and E11); the serekh was surmounted by a falcon facing left. [J. Kahl 1994 corpus 3332; Kahl et al., 1995, 164].
A different writing, with only the leg, was reported by Ricci in 1820 and by Lepsius in 1858 (this latter's one was without falcon of the serekh, Konigsbuch n.905); Kurt Sethe briefly discussed this king's status in a note of an article in Z.A.S. 35 (1899, p.6,7 n.4). Now, because at the half of the twentieth century M. Cerny found the manuscript of Ricci in Banks Manuscript XX A.I (of the Wadi Maghara inscriptions of Sekhemkhet), Swelim asks if the source of Lepsius could have been a completely different one from Ricci's (op. cit p. 183; also see Cerny, The inscriptions of Sinai, 1955 p. 55-6).
The probable presence in Sinai would increase the possibility that this Ba was a short reigning king of the period of Netjerykhet, Sanakht and Sekhemkhet. This king should therefore have reigned in the obscure period of the middle 3rd dynasty.
Indeed the question about this name is more complex: in the publications of the Sinai inscriptions (Gardiner, Peet, Cerny), J. Cerny pointed out that the leg sign was indeed a misinterpretation of Ricci's rough sketch representing the Horus name of Sanakht (vertical Sa and horizontal n united and read as the b sign) [cf. Baud, 2002, 20] on the relief now in Cairo Museum.
Thus the only source actually remaining to witness the existence of a Early Dynastic king Horus Ba is the Saqqara slab found by Firth in the funerary complex of Netjerykhet at Saqqara, unless Swelim's hypothesis that Lepsius' source (serekh without falcon) was different from Ricci's MS had to be demonstrated by further data.
J. von Becherath, in his Handbuch der Ag. Konigsnamen (1984) p. 49 doubiously identifies king Ba (Foot + Ram), with the one we have here named BIRD; some scholars have recently followed him (Wilkinson, Early Dynastic Egypt), but the two Horus names in question must belong to different rulers, and we have precised that there's no indication that the bird in Horus Bird's serekh is a Ba, because too few details are drawn.
Swelim places Horus Ba as one of the 4 predecessors of Djoser (but it's unprobable that, as the Egyptian archaeologist theorizes, 4 kings with long reigns separated Djoser from Khasekhemwy): to Ba he attributes the Ptahhotep enclosure at Saqqara, west of the Step Pyramid complex (see the table in the Third Dyn. page).
Nabil Swelim adds a further interesting note on the possible later cult of king BA which would be suggested by the name of NiankhBA whose tomb, south of Djoser's complex nearby to that of Nebkauhor - Idu, is close to the entrance of Ninetjer's gallery, north of the Unas causeway (Nabil Swelim, 'The Dry moat of the Netjertkhet complex', in Baines et al. ed., Pyramid Studies and other essays presented to I.E.S. Edwards, 1988 p. 12-22, fig. 4), and in the same area of another tomb whose owner has the name formed with that of the IIIrd Dynasty king Nebka: NiankhNebka.
The site was originally the early Second Dynasty kings royal necropolis (tombs A, B - Hotepsekhemwy and Ninetjer): this would argue also in favour of the possibility that the mentioned individuals were priests charged with duties of the cult of earlier kings buried in the area. South of tombs A and B a new one, tomb C (reused by the 18th dynasty priest of Aton Meryre) has been cleared early in 2002 by a Dutch mission (van Walsem, Raven).
Therefore, as stated above, Ba could even be the Horus name of one of the Second Dynasty kings whose Nswtbity/Nebty are found on few Memphite sources: Wneg, Sened, Nwbnefer, Neferkasokar; in the same way as the Horus name Za (cf. Wneg) which has not yet been linked to any Nebty/Nswtbity name. Curiously, the NK lists report Ba-NTrw or Ba-Njnetjer as cartouche name of Njnetjer; in the Abydos list BA is written with the ram hieroglyph .
*The first occurrance of the standing ram hieroglyph (Gardiner E10/11, Khnwm / Ba) seems to be that on the Narmer baboon in Berlin (Staatl. Mus., 22607: Kahl, 1994, Quelle 125, bibl. p. 472-473), after which it appears rather frequently especially since late 1st Dynasty and mid-2nd Dynasty (under Qa'a / Sneferka; under Za and especially Ninetjer (Khnwmenjj, Khnwmhotep): cf. Lacau-Lauer, PD V, 3ff., 31ff., 47, 39). [F. Raffaele]